Page 371 - Mechanics Analysis Composite Materials

356 Mechanics and analysis of composite materials

last three equations of Eqs. (7.23) in which M, =My =Mxev= 0 form a set of
homogeneous equations whose solution is K~T= K~T= xXy~= 0. This means that a
flat symmetricpanel does not acquire curvature in the process of cooling. Naturally,
the in-plane dimensions of the panel become different from those that the panel had
before cooling. The corresponding thermal strains &:T,~:T and y:yT can be found
from the first three equations of Eqs. (7.23) in which N, = N, =Nxy =0, but
N: ,N& and N& are not zero.
However, for unsymmetric laminates, in general, A42n # 0, and these laminates
experience bending and warping in the process of cooling. To demonstrate this,
consider two antisymmetric laminates studied in Section 5.7.
The first is a two-layered orthotropic cross-ply laminate shown in Fig. 5.13.
Using stiffness coefficients calculated in Section 5.7, taking into account that for a
cross-ply laminate NL =MT2 = 0, and applying Eqs. (7.23) for Nxy and Mxy we get
y:yT = 0 and Kxy~= 0. Thus, cooling of the cross-ply laminated panel does not
induce its in-plane shear and twisting. The other four of Eqs. (7.23) acquire the
form:

(7.74)

where

The solution of Eqs. (7.74) can be written as

(7.75)

(7.76)